We can apply exactly the same strategy to a whole

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Calculated their ratio, which he called the resistance. We can apply exactly the same strategy to a whole electric circuit, mentally reducing it to a single resistor, even though the given circuit is as complicated as your cell phone or laptop: see Figure 1. Figure 1. Measurements of the total current through a circuit as function of the total voltage applied to this circuit, and calculation of their ratio yield the equivalent conductance (or the equivalent resistance), which effectively reduces the entire circuit to a single resistor. The ratio of the total voltage applied to the circuit to the total current that flows through this circuit is equal, by definition, to the equivalent resistance of this circuit: ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? = ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵?࠵?࠵?࠵? ࠵? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? [Equation 1] The equivalent conductance is reciprocal of the equivalent resistance. ࠵? !" = ࠵? !"#$% ࠵? !"#$% ; ࠵? !" = 1 ࠵? !" = ࠵? !"#$% ࠵? !"#$% [Equation 2] The concept of equivalent resistance is very convenient if we need only “the big picture” such as ü How much power the entire circuit absorbs ü How much current does it draw from a battery ü What is the battery service time for powering this circuit, etc. It is much easier to use the equivalent resistance for power calculations than to calculate the power absorbed by each circuit element and sum up all the results. <Sidebar> The concept of equivalent resistance (or conductance) simplifies finding the “bulk” parameters of a circuit such as the total power consumption, the battery service time for powering this circuit, etc. Book Page 61
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EE for the 21 st century Review the basics 1-1-6 Equivalent resistance © 2015 Alexander Ganago Page 3 of 11 Last printed 2015-07-24 6:22 PM File: 2015 1-1-6 R_eq.docx Experimentally, finding the equivalent resistance is straightforward, as outlined at the very beginning of this Unit; many power supplies have built-in voltmeters and ammeters, which display the total voltage applied to the circuit and the total current that flows through this circuit. <Sidebar> Experimentally, to find the equivalent resistance of a circuit: ü Apply a certain voltage to the circuit ü Measured the current through this circuit, and ü Calculate their ratio. The challenge is to determine the equivalent resistance analytically, from a given circuit diagram. Two scenarios are possible: 1) If the circuit is reducible to series and parallel combinations of resistors, apply the results obtained in Unit 1-1-5 2) If the circuit is not reducible to series and parallel combinations of resistors, use general methods for circuit analysis such as Node voltage equations, which are explained later in the course.
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  • Fall '07
  • Ganago
  • Electric charge, Alexander Ganago

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